Environment

• Qiskit version: 2.0.0 and 1.3.2
• Python version: 3.12.8
• Operating system: Linux(Fedora)

What is happening?

Commutation Checker fails when checking the commutativity of a large PauliGate. It has to do with the fact that it tries to construct its tensor representation and for some reason runs out of indices to iterate over (I am not really sure what is causing that). This is specially sad because in most cases checking the commutativity of a Pauli String should be trivial regardless of its size.

How can we reproduce the issue?

from qiskit.circuit import QuantumCircuit
from qiskit.circuit.commutation_library import SessionCommutationChecker as scc
from qiskit.converters import circuit_to_dag

circuit = QuantumCircuit(9)
circuit.pauli("ZZZZZZZZZ", range(9))
circuit.cx(5, 6)

dag = circuit_to_dag(circuit)
nodes = list(dag.topological_op_nodes())
print(scc.commute_nodes(nodes[0], nodes[1], max_num_qubits=10))

What should happen?

And I get the following error:

thread '<unnamed>' panicked at crates/accelerate/src/unitary_compose.rs:114:67:
index out of bounds: the len is 26 but the index is 26
note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace
Traceback (most recent call last):
  File "/home/marc/Documents/QiskitPRs/issue.py", line 11, in <module>
    print(scc.commute_nodes(nodes[0], nodes[1], max_num_qubits=10))
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/marc/pyenvs/windsurfer/lib64/python3.12/site-packages/qiskit/circuit/commutation_checker.py", line 45, in commute_nodes
    return self.cc.commute_nodes(op1, op2, max_num_qubits)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
pyo3_runtime.PanicException: index out of bounds: the len is 26 but the index is 26

Any suggestions?

I suggest that the commutativity checker becomes Pauli based. By that I mean that most gates diagonalize in the same basis as a Pauli, so we should check the commutativity of the associated Pauli which is a very cheap operation when done efficiently (bitwise). For instance, one can associate a CNOT gate with a ZX Pauli or a S gate with a Z Pauli. Some other cases are less trivial, like for the H gate, where we need to decompose it into X+Z and checking the commutativity is slightly more involved. However, it should still be a much faster operation than instantiating the matrix of the operation, and if we speed up the Pauli commutativity would probably be as fast as a lookup table.